Mathematics
Geometric Progression
गुणोत्तर श्रेणी
In this Class 9 Mathematics topic from Sequences and Progressions, students explore sequences in which each term is obtained by multiplying the preceding term by a fixed number. They learn to identify the common ratio, distinguish a geometric progression from other patterns, write its terms, and use the general term to find a specific position in the sequence. Examples help connect the idea with repeated growth, decrease, and everyday numerical patterns.
Practice questions
What is the fifth term of the sequence \(\frac{5}{6},\frac{5}{3},\frac{10}{3},\frac{20}{3},\ldots\)?MediumLevel 55What is the sixth term of the geometric progression (243,81,27,9,\ldots)?MediumLevel 55Which of the following sequences is a geometric progression with common ratio \(-2\)?MediumLevel 55Which option has common ratio (\frac{1}{3})?MediumLevel 55In the geometric progression \(5,25,125,625,\ldots\), which term is \(3125\)?MediumLevel 55If \(a_n=27\left(\frac{1}{3}\right)^{n-1}\), what is \(a_4\)?MediumLevel 55If (4,16,x,256) is a geometric progression, what is (x)?MediumLevel 55What is the sum of the first (4) terms of the geometric progression (14,28,56,112,\ldots)?MediumLevel 55Which of the following sequences is a geometric progression in which each term is three times the immediately preceding term?MediumLevel 55What is the (n)th term of the sequence (12,36,108,324,\ldots)?MediumLevel 55If a = 3 and r = 2, what will be the sum of the first 6 terms?MediumLevel 55If \(a_1=30\) and \(r=\frac{1}{3}\), what is \(a_3\)?MediumLevel 55Which value of (x) makes (8,40,x) a geometric progression?MediumLevel 55In the sequence (6,24,96,384,\ldots), which term is (1536)?MediumLevel 55If \(a_2=16\) and \(a_5=1024\), and the ratio is positive, what is \(r\)?MediumLevel 55What is the fifth term of the geometric progression \(5,-15,45,-135,\ldots\)?MediumLevel 55Which option has the first four terms of a geometric progression with (a=7) and (r=4)?MediumLevel 55If (6,18,54,\ldots) is a geometric progression, what is the product of the first three terms?MediumLevel 55What is the next term in the geometric progression (90,30,10,\ldots)?MediumLevel 55If (a_n=8\cdot2^{n-1}), which sequence does it form?MediumLevel 55